Abstract
We consider the dynamical properties of dissipative continuous-time quantum walks on directed graphs. Using a large-deviation approach we construct a thermodynamic formalism allowing us to define a dynamical order parameter, and to identify transitions between dynamical regimes. For a particular class of dissipative quantum walks we propose a quantum generalization of the the classical PageRank vector, used to rank the importance of nodes in a directed graph. We also provide an example where one can characterize the dynamical transition from an effective classical random walk to a dissipative quantum walk as a thermodynamic crossover between distinct dynamical regimes.
1 More- Received 29 May 2012
DOI:https://doi.org/10.1103/PhysRevA.86.032342
©2012 American Physical Society